An investigation into trends in competitive balance in the NBA.

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Question 2

Outline two measures that can be used to estimate competitive balance within professional team sports.  

Apply one of these measures to a professional team sport of your choice (in a country of your choice).  Collect data (i.e. team performance information) for your chosen sport, for approximately the last 50 years.  

Examine and assess how competitiveness has varied over time and establish the extent (if any) to which this can be related to structural changes to the sport (such as league format changes, intervention policies etc).    

Question 2

(i) Competitive Balance measure 1: Ratio of Standard Deviations (RSD)

         where         and        

G = no of games played, N = number of teams in the league, wp = win percentage, wpikt is the win percentage of team i, in league k, for season t.

is the mean win percent and is a positive constant. For a sport such as basketball, where a team can only win or lose games, this will equal 0.5.

is the standard deviation of wins in a perfectly balanced league i.e. each team is of equal strength and has an equal probability of winning. This number declines as the number of games (G) played in the league increases.

is the standard deviation of wins in the actual league

represents the ratio of standard deviations. This compares the performance of an actual league when compared to that of the ideal league. A perfectly balanced league would correspond to RSD = 1 where . Competitive balance worsens when RSD increases, as the dispersion of winning percentage of the actual league grows relative to that of the ideal league.

RSD has been used extensively throughout the literature, first developed by Noll (1988) and Scully (1989) it has been employed by Quirk and Fort (1997), Berri et al. (2005), Fort and Lee (2007) amongst others.

The major shortcoming of the metric as detailed by Humphreys (2002) is that it does not capture relative standings of teams within a division. Thus, there might be two leagues with identical RSDs, but with one league where one team exhibits long run domination by consistently winning the league and one where this does not occur.

To complement this measure, a dynamic season to season measure such as that developed by Buzzacchi et al. (2003), would better be able to assess long run domination over time.

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Competitive Balance measure 2: Dynamic measure developed by Buzzacchi et al. (2003). The model for a closed league (no promotion/relegation) is derived as follows.

In a perfectly competitive league, the probability a team will finish in any position of a league for one season is, where n is the number of teams.

Therefore the probability a team will place in the top k places of the league is  

The probability a team will have placed at least once in the top k positions after T seasons is given by

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